1. Field of the Invention
This invention relates to arrangements for sharpening the frequency response characteristics of a filtering function. The invention relates in particular to arrangements for subjecting a signal to multiple passes through a signal processing function to achieve a frequency response characteristic that is sharper than that which can be achieved by a single pass through the same function.
2. Description of the Prior Art
It often happens that a filter frequency response characteristic is needed which is beyond the capabilities of a hardware filter that is at hand for a circuit designer or a software filter function that is at hand for a computer programmer who is designing a program to simulate a signal processing system. For example, a circuit designer may need a filter function having greater stopband loss and possibly less passband variation about the desired transmission level than can be achieved with a single filter unit which is at hand. In typical prior art arrangements wherein a plurality of such units are combined in order to improve the characteristics in one of the relevant bands, it usually occurs that the filter response in another one of the bands is significantly impaired, and this situation prevails regardless of whether the desired change is increased loss or reduced passband variation. In many instances the designer or the programmer may not have the time or the technological facility to design a new filter or a new subroutine, as the case may be, to meet the new filtering requirements. Alternatively, at least the hardware circuit designer may anticipate a circuit production need that is insufficient to warrant the expense of redesign, especially if the filter is an integrated circuit chip, as is often the case for certain filtering situations in the present state of the art.
As already noted, it is known in the art to subject a signal to multiple passes through a given function, e.g., by using tandem filter chips of like characteristics, or by using successive applications of a known filtering software subroutine, or using successive passes of the signal through a single filter section with appropriate delays between passes. However, in such response-sharpening arrangements the multiple applications of a given filter function usually improve the response in one aspect at the expense of deteriorated response in another aspect. This is also true of prior proposals for systems in which so-called smooth and rough resultants of a filtering operation are again subjected to a smoothing operation. A smooth resultant is the normal filter section output and the rough resultant is a signal corresponding to the energy portion removed to get the smooth resultant, i.e., the rough resultant is the resisual.